This section describes how to calculate quantities used in the carbon balance error verification described in § 1065.543 . Paragraphs (a) through (c) of this section describe how to calculate the mass of carbon for a test interval from carbon-carrying fluid streams, intake air into the system, and exhaust emissions, respectively. Paragraph (d) of this section describes how to use these carbon masses to calculate four different quantities for evaluating carbon balance error. Use rectangular or trapezoidal integration methods to calculate masses and amounts over a test interval from continuously measured or calculated mass and molar flow rates.
Where:
j = an indexing variable that represents one carbon-carrying fluid stream.
N = total number of carbon-carrying fluid streams into the system over the test interval.
wC = carbon mass fraction of the carbon-carrying fluid stream as determined in § 1065.655(d) .
mfluid = the mass of the carbon-carrying fluid stream determined over the test interval.
Example:
N = 2
wCfuel = 0.869
wCDEF = 0.065
mfuel = 1119.6 g
mDEF = 36.8 g
mCfluid = 0.869·1119.6 + 0.065·36.8 = 975.3 g
Where:
MC = molar mass of carbon.
nint = measured amount of intake air over the test interval.
xCO2int = amount of intake air CO2 per mole of intake air.
Example:
MC = 12.0107 g/mol
nint = 62862 mol
xCO2int = 369 [MICRO]mol/mol = 0.000369 mol/mol
mCair = 12.0107·62862·0.000369 = 278.6 g
Where:
MC = molar mass of carbon.
nexh = calculated or measured amount of raw exhaust over the test interval.
xH2Oexh = amount of H2O in exhaust per mole of exhaust.
xCO2int = amount of intake air CO2 per mole of intake air.
xdil/exhdry = amount of excess air per mole of dry exhaust. Note that excess air and intake air have the same composition, so xCO2dil = xCO2int and xH2Odil = xH2Oint for the chemical balance calculation for raw exhaust.
xint/exhdry = amount of intake air required to produce actual combustion products per mole of dry exhaust.
Example:
MC = 12.0107 g/mol
nexh = 62862 mol
xH2Oexh = 0.034 mol/mol
xCO2int = 369 [MICRO]mol/mol = 0.000369 mol/mol
xdil/exhdry = 0.570 mol/mol
xint/exhdry = 0.465 mol/mol
mCair = 12.0107·62862·(1 - 0.034)·0.000369·(0.570 + 0.465) = 278.6 g
Where:
MC = molar mass of carbon.
nexh = measured amount of raw exhaust over the test interval.
xCO2int = amount of intake air CO2 per mole of intake air.
Example:
MC = 12.0107 g/mol
nexh = 62862 mol
xCO2int = 369 [MICRO]mol/mol = 0.000369 mol/mol
mCair = 12.0107·62862·0.000369 = 278.6 g
Where:
MC = molar mass of carbon.
ndexh = measured amount of diluted exhaust over the test interval as determined in § 1065.642 .
ndil = measured amount of dilution air over the test interval as determined in § 1065.667(b) .
xCO2int = amount of intake air CO2 per mole of intake air.
Example:
MC = 12.0107 g/mol
ndexh = 942930 mol
ndil = 880068 mol
xCO2int = 369 [MICRO]mol/mol = 0.000369 mol/mol
mCair = 12.0107·(942930 - 880068)·0.000369 = 278.6 g
Where:
MC = molar mass of carbon.
mCO2 = mass of CO2 over the test interval as determined in § 1065.650(c) .
MCO2 = molar mass of carbon dioxide.
mCO = mass of CO over the test interval as determined in § 1065.650(c) .
MCO = molar mass of carbon monoxide.
mTHC = mass of THC over the test interval as determined in § 1065.650(c) .
MTHC = effective C1 molar mass of total hydrocarbon as defined in § 1065.1005(f)(2) .
Example:
MC = 12.0107 g/mol
mCO2 = 4567 g
MCO2 = 44.0095 g/mol
mCO = 0.803 g
MCO = 28.0101 g/mol
mTHC = 0.537 g
MTHC = 13.875389 g/mol
Where:
mCexh = mass of carbon in exhaust emissions over the test interval as determined in paragraph (d) of this section.
mCfluid = mass of carbon in all the carbon-carrying fluid streams flowing into the system over the test interval as determined in paragraph (a) of this section.
mCair = mass of carbon in the intake air flowing into the system over the test interval as determined in paragraph (b) of this section.
Example:
= 1247.2 g
= 975.3 g
= 278.6 g
= 1247.2 - 975.3 - 278.6
= -6.7 g
Where:
t = duration of the test interval.
Example:
= -6.7 g
t = 1202.2 s = 0.3339 hr
= -20.065 g/hr
Example:
= -6.7 g
= 975.3 g
= 278.6 g
= -0.0053
Where:
i = an indexing variable that represents one test interval.
N = number of test intervals.
WF = weighting factor for the test interval as defined in the standard-setting part.
mCexh = mass of carbon in exhaust emissions over the test interval as determined in paragraph (c) of this section.
mCfluid = mass of carbon in all the carbon-carrying fluid streams that flowed into the system over the test interval as determined in paragraph (a) of this section.
mCair = mass of carbon in the intake air that flowed into the system over the test interval as determined in paragraph (b) of this section.
t = duration of the test interval. For duty cycles with multiple test intervals of a prescribed duration, such as cold-start and hot-start transient cycles, set t = 1 for all test intervals. For discrete-mode steady-state duty cycles with multiple test intervals of varying duration, set t equal to the actual duration of each test interval.
N = 2
= 1/7
= 6/7
= 1255.3 g
= 1247.2 g
= 977.8 g
= 975.3 g
= 280.2 g
= 278.6 g
= -0.0049
N = 2
= 0.85
= 0.15
= 2.873 g
= 0.125 g
= 2.864 g
= 0.095 g
= 0.023 g
= 0.024 g
= 123 s
= 306 s
= -0.0047
40 C.F.R. §1065.643